No, but I have some concerns over your employment status when you refer to it as "taking another self-employed POSITION with a different company".
Employment status may be an area you need to look into further.
Irrespective of Off-Payroll rules, the company appointing you may still be at risk if an HMRC inspection deems your self-employment relationship to be Employment, so it is important that your contracts and working arrangements reflect your Self Employment status.
It may not be relevant, but your name is zltd. Are you working through a limited company?I am already registered as self-employed with HMRC. Due to COVID I have also signed up with a number of apps to carry out odd job and inspections and have an agreement stating I am self-employed to carry out task via their company.
However, when completing self-assessment online, it always asks whether I am self-employed with any other business.